Generating usable output-entanglement in continuous variable systems can serve as a viable resource for improving applications in quantum information science. In this work, we show how to generate steady-state output-entanglement in a two-stage conversion setup between optical and microwave photon which employs resonantly coupled magnetic and mechanical excitations, as proposed in Phys. Rev. Applied 18, 044059 (2022). We show that the entanglement can be maximized for the same set of parameters which optimize the frequency-conversion efficiency, and that it can be leveraged for a teleportation-based state-transfer protocol for coherent input-states with fidelity close to unity. We propose an implementation based on an Yittrium Iron Garnet disk of micrometer scale, and use both simulation results and reasonable estimates to assess the performance under optimized conditions. We find a maximum teleportation fidelity of $0.75$ for the proposed setup.

We develop an $\mathrm{L}^p$-Banach noncommutative-geometric framework for Dolbeault-Dirac operators on compact Kähler manifolds with coefficients in a Hermitian holomorphic vector bundle $E$. For every $p \in (1,\infty)$, we prove that the closed $\mathrm{L}^p$-realization $\mathcal{D}_{E,p}$ of the Dolbeault-Dirac operator is bisectorial and admits a bounded $\mathrm{H}^\infty$ functional calculus on $\mathrm{L}^p(Ω^{0,\bullet}(M,E))$. We also show an $\mathrm{L}^p$-Gaffney-type estimate, obtain $\mathrm{L}^p$-Hodge decompositions, and prove that $\mathcal{D}_{E,p}$ gives rise to an even compact Banach spectral triple over the algebra $\mathrm{C}(M)$, graded by form parity. The index of the associated Fredholm operator is equal to the holomorphic Euler characteristic $χ(M,E)$. In particular, it is independent of $p$. A central tool is an abstract notion of Ricci curvature lower bound for strongly continuous semigroups on $\mathrm{UMD}$ Banach spaces, formulated as a semigroup-level intertwining relation. Under this condition, together with natural Riesz equivalences and bounded $\mathrm{H}^\infty$ functional calculi for the relevant generators, the associated Hodge-Dirac operator is bisectorial and admits a bounded $\mathrm{H}^\infty$ functional calculus. The framework also applies to heat semigroups on Riemannian manifolds, $q$-Ornstein-Uhlenbeck semigroups and semigroups of Schur multipliers. This provides a unified Banach-space approach to curvature, functional calculus, Riesz transforms and index theory beyond the Hilbert space setting.

The Optimum-Path Forest is a graph-based framework for designing classifiers that exploit inter-sample connectivity. A particular variant constructs decision boundaries based on prototypes computed by a Minimum Spanning Tree (MST) over the training data, which might become prohibitive for large-scale datasets. In this context, Quantum Machine Learning has emerged as a promising approach to overcome the high computational burden of combinatorial problems. We propose a quantum-inspired approach for prototype selection in OPF classifiers by reformulating the MST problem as a Polynomial Unconstrained Binary Optimization (PUBO) task and further employing the Feedback-Based Quantum Optimization (FALQON) algorithm for Hamiltonian minimization. The PUBO formulation reduces the need for qubits and eliminates the need for auxiliary variables, thereby addressing scalability constraints in current quantum hardware. Experiments on real-world datasets demonstrate that the FALQON-optimized MST achieves accuracies comparable to those of the classical Prim's algorithm while maintaining prototype quality. While FALQON occasionally reached local minima, it did not significantly impact the accuracy of the prototype selection process.

A direct coupling between the inflaton and Standard Model gluons can dynamically raise the QCD confinement scale during inflation, making the axion temporarily heavy and suppressing axion isocurvature perturbations. As inflation proceeds, the confinement scale relaxes, the axion becomes light, and late-time de Sitter fluctuations can generate the observed dark matter abundance. We analyze this mechanism without specifying an inflationary potential, instead parametrizing the background by $ε(N) \propto 1/N^p$, where $N$ is the number of $e$-folds before the end of inflation. The single parameter $p$ distinguishes monomial models ($p=1$), standard plateau models ($p=2$), and ultra-flat plateau or hilltop-like models ($p\ge 3$). We analytically show that the mechanism selects plateau-like ($p\ge 2$) inflation: monomial models generically cause the confinement scale to grow too rapidly, while plateau models keep the QCD sector under perturbative control. In the minimal scenario, reheating occurs through the same inflaton-gluon coupling, and viable axion dark matter production is obtained when deconfinement occurs after the CMB window. The early-confinement sector also generically shifts the scalar spectral index to smaller, redder values. Because ultra-flat ($p \ge 3$) models inherently predict overly red spectra, this shift exacerbates their tension with CMB data, leaving $p=2$ plateau models as the phenomenologically viable parameter space (in this parametrization).

It is shown that in all types of metallic magnets the coupling of the order parameter to the conduction electrons leads to an order-parameter susceptibility that is long-ranged at zero temperature. This is true for all known classes of ferromagnets, and also for antiferromagnets and spin-density wave systems, helimagnets, magnetic nematics, and altermagnets. The consequences for the magnetic quantum phase transition vary between different classes of magnets. In almost all 3-d systems with a homogeneous magnetization, as well as in magnetic nematics and in altermagnets, the long-ranged correlations generically modify the nature of the magnetic quantum phase transition from second order to first order. The only exception are non-centrosymmetric ferromagnets with a strong spin-orbit interaction, where the correlations change the order of the transition in 2-d systems, but not in 3-d ones. In helimagnets, spin-wave systems, and Neel antiferromagnets their effect is even weaker and does not change the order of the transition if the ordering wave number is sufficiently large, except in flat-band systems. In systems with quenched disorder the transition generically is of second order, but the correlations modify the critical behavior. These conclusions are reached by very simple considerations that are based entirely on the single-particle excitations in the nonmagnetic phase and their modifications by a field conjugate to the order parameter, augmented by renormalization-group considerations.

In this work, we propose a continuous-variable quantum algorithm to compute the projection coefficients of a holomorphic function in the Segal--Bargmann space by leveraging its isometric correspondence with single-mode quantum states. Using CV quantum circuits, we prepare the state $\ket{f}$ associated with $f(z)$ and extract the coefficients $c_n = \braket{n}{f}$ via photon-number-resolved detection, enhanced by interferometric phase referencing to recover full complex amplitudes. We detail the construction of the state-preparation oracle for various functional classes and analyze the protocol's robustness under realistic noise models, including detector inefficiency and state preparation errors. This enables direct quantum estimation and visualization of the coefficient sequence -- offering a hardware-native protocol for characterizing non-Gaussian states and analyzing functions defined by quantum oracles, complementary to classical numerical integration.

The radio galaxy NGC 1275 is the Brightest Cluster Galaxy in the Perseus cluster. It is well-studied across all wavebands, including Very High Energy (VHE; E>100GeV gamma-rays, and with radio observations over the last 20 years tracking an unusual radio component, "C3". NGC 1275 was observed in an exceptional VHE flaring state between 2016 December 31 and 2017 January 3. The flare peak reached ~1.5 Crab units as measured by the MAGIC observatory. We report on the observations of NGC~1275 conducted by VERITAS and multi-wavelength data collected during this flaring state, and for context, data taken between 2009 and 2017 inclusive. VERITAS detected the declining state of the flare on 2017 January 2 (MJD 57755) and 3 (MJD 57756) at an average flux state of 0.5 Crab units. VERITAS spectra show an overall long-term trend of harder-when-brighter. During the flare, the gamma-ray spectrum obtained from the combined Fermi-LAT, MAGIC, and VERITAS observations, changes from a power law with an exponential cut-off on January 1 to a log-parabola on January 2. To study the evolution of the flare in more detail, multi-band spectral energy distributions (SEDs) were constructed for the nights of 2017 January 1 and 2 corresponding to the shift from the peak to the decline of the flare. A blob-in-jet modeling of the SEDs results in support for a two-component model with a jet angle of 10 degrees to the line of sight and the gamma-ray emission zone located in the vicinity of the C3 radio component.

Let $G$ be a group and let $R$ be a $G$-graded ring. We show that every nonzero central idempotent in $R$ has finite support group in two broad settings: when $G$ is abelian, and when $G$ is arbitrary but the grading satisfies a certain one-sided non-annihilation condition on nonzero homogeneous elements. In particular, under the respective hypotheses, if $G$ is torsion-free, then every central idempotent lies in the principal component of the grading. Our results generalize earlier results by H. Bass, R. G. Burns, and A. A. Bovdi--S. V. Mihovski, from group rings and crossed products, to non-commutative, possibly non-unital, group-graded rings. We demonstrate the utility of our results by applying them to semigroup-graded rings, Leavitt path rings, fractional skew monoid rings, partial skew group rings, and algebraic Cuntz-Pimsner rings.

We extend the CCSDTQ implementation in CFOUR to UHF and ROHF references and demonstrate its efficiency. We apply it to basis set convergence of post-CCSDT(Q) corrections for the W4-08 thermochemical dataset. Convergence of (Q)$_Λ$--(Q) is relatively rapid. For difficult species (e.g., B2, O3), CCSDTQ--CCSDT(Q)$_Λ$ may converge more slowly than (5)$_Λ$, but the effects and and basis-set trends oppose each other. Consequently, a single-shot CCCSDTQ(5)$_Λ$-CCSDT(Q)$_Λ$ correction appears most efficient. For radicals with bifurcating UHF solutions, energetics of the `less spin-contaminated' solution are clearly more well-behaved. Our best computed adiabatic electron affinity of ozone is in excellent agreement with experiment.

Accelerating materials development requires quantitative linkages between processing, microstructure, and properties. In this work, we introduce a framework for mapping microstructure onto a low-dimensional material manifold that is parametrized by processing conditions. A key innovation is treating microstructure as a stochastic process, defined as a distribution of microstructural instances rather than a single image, enabling the extraction of material state descriptors that capture the essential process-dependent features. We leverage the manifold hypothesis to assert that microstructural outcomes lie on a low-dimensional latent space controlled by only a few parameters. Using phase-field simulations of spinodal decomposition as a model material system, we compare multiple microstructure descriptors (two-point statistics, chord-length distributions, and persistent homology) in terms of two criteria: (1) intrinsic dimensionality of the latent space, and (2) invertibility of the processing-to-structure mapping. The results demonstrate that distribution-based descriptors can recover a two-dimensional latent structure aligned with the true processing parameters, yielding an invertible and physically interpretable mapping between processing and microstructure. In contrast, descriptors that do not account for microstructure variability either overestimate dimensionality or lose predictive fidelity. The constructed material manifold is shown to be locally continuous, wherein small changes in process variables correspond to smooth changes in microstructure descriptors. This data-driven manifold mapping approach provides a quantitative foundation for microstructure-informed process design and paves the way toward closed-loop optimization of processing--structure--property relationships in an integrated materials engineering context.

Sunspots are transient, magnetically intense features that host oscillations linked to magnetohydrodynamic (MHD) waves. These waves may contribute to plasma heating and drive mass flows in the solar wind. Beyond their energetic role, they serve as diagnostic tools for probing sunspot structure. In this study, we investigated chromospheric wave propagation in a sunspot using high-resolution, multi-wavelength observations from the Goode Solar Telescope at Big Bear Solar Observatory. Spectral analysis shows that the intensity at H$α$ line core and its wings exhibited oscillatory signal at about 3 min. We performed a cross-wavelet analysis to examine the phase relationship between the wing-integrated and line-core intensity oscillations of the H$α$ line and the centroid-derived H$α$ Doppler velocity. We also analyze the phase relationships between intensity pairs from different passband combinations of the H$α$ line. The results indicate the presence of slow magnetoacoustic modes manifesting standing waves along with upward propagating waves. The observed phase patterns suggest that umbral waves are confined within a non-ideal acoustic resonator, providing measurable wave properties that could serve as input for sunspot seismology and refine models of sunspot atmospheric structure.

We study the classification of the gapped phases or massive renormalization group (RG) flows dual to the massless RG flows under changing the sign of the coupling constants. Whereas our formalism is based on combining Higgs- or Nambu-Goldstone-type arguments with Cardy's smeared boundary conformal field theories (SBCFTs), several puzzling structures arise. More specifically, the established Higgs or Nambu-Goldstone type arguments on the duality imply that the natural basis for the gapped states should be constructed from a set of smeared Ishibashi states, which are unphysical in boundary critical phenomena. Hence, the module of the gapped phases can be outside of that of boundary critical phenomena, whereas one can still calculate characterizing quantities by applying SBCFTs to the models. For example, we demonstrate that the massive RG flow dual to the massless RG flow from the tricritical Ising model to the Ising model, one of the simplest massless RG flows, has this unusual structure. This can be regarded as a quantum field-theoretic analogue of order-disorder coexistence in lattice models. More generally, the resultant gapped phases usually spontaneously break non-group-like symmetry (or noninvertible symmetry). Our work provides systematic quantum field theoretic descriptions of such unusual phases with spontaneous symmetry breaking of non-group-like (or noninvertible) symmetries.

We investigate the correlation between star formation rate (SFR) surface density and gas surface density (known as the Kennicutt-Schmidt, KS, relation) at kiloparsec (kpc) scales across cosmic time ($0\le z \le 8$) for galaxies with stellar masses $>10^9\,\rm M_{\odot}$, using the COLIBRE state-of-the-art cosmological hydrodynamical simulations. These simulations feature on-the-fly non-equilibrium chemistry coupled to dust grain evolution and detailed radiative cooling down to $\approx 10$~K, enabling direct predictions for the atomic (HI) and molecular (H$_2$) KS relations. At $z\approx 0$, COLIBRE reproduces the observed (spatially-resolved) KS relations for HI and H$_2$, including the associated scatter, which we predict to be significantly correlated with stellar surface density, local specific SFR (sSFR), and gas metallicity. We show that the HI KS relation steepens for lower-mass galaxies, while the H$_2$ KS relation shifts to higher normalisation in galaxies with higher sSFRs. The H$_2$ depletion time decreases by a factor of $\approx 20$ from $z = 0$ to $z = 8$, primarily due to the decreasing gas-phase metallicity. This results in less H$_2$ and more HI being associated with a given SFR at higher redshift. We also find that galaxies with higher sSFRs have a larger molecular gas content and higher star formation efficiency per unit gas mass on kpc scales. The predicted evolution of the H$_2$ depletion time and its correlation with a galaxy's sSFR agree remarkably well with observations in a wide redshift range, $0\le z\le 5$.

James Webb Telescope (JWST) observations have unveiled numerous galaxy candidates between $z \sim 9 - 16.5$, hinting at an over-abundance of sources at the bright-end of the UV luminosity function (UV LF) at z $\gsim$ 11. Complementarily, the Atacama Large Millimetre Array (ALMA) has been yielding dust mass estimates at $z \sim 5 - 7$. In this work, we develop an analytic formalism baselined against ALMA results, jointly exploring the impact of bursty star formation and its associated dust enrichment, on the visibility of early galaxies, while also modelling sources scattered off the main sequence of star formation. We incorporate dust production in type II Supernovae, dust destruction, ejection, growth and sputtering. Our key results are: (i) explaining the UV LF at $z \sim 5 - 13$ requires an average star formation efficiency that evolves as $f_*(z) = 10^{0.13z-3.5}$, with a number of observations exceeding this main sequence by a factor of 10; (ii) The dust enrichment of early systems is driven by dust production in SNII ejecta, while growth and sputtering impact the dust mass by 60\% and 40\% respectively at $z \sim 7$; (iii) galaxies at $z \gsim 9$ can retain significant dust, reaching average dust-to-stellar mass ratios of 0.19\% (0.14\%) at $z \sim 9$ ($z \sim 11$). Dust attenuation decreases with redshift as dust becomes increasingly dispersed within halos; (iv) observations by ALMA at $z \sim 5$ and 7 are not representative of the average population that makes up the UV LF; (v) assuming all stars to have formed instantaneously results in a high light-to-mass ratio. This naturally results in our model yielding a lower limit on the stellar mass contained in a halo, also under-predicting the observed stellar mass function.

The absence of global symmetries in a quantum gravity theory often requires the introduction of (new) symmetry-breaking defects, which appear as singular objects in the low-energy description. This has been formalized in the Cobordism Conjecture, which further relates the asymptotics of these defects to non-trivial deformation classes of the effective theory. In this work we investigate the symmetry-breaking defects for theories with a discrete symmetry $G$ encoded in the bordism groups $Ω^ξ_2 (BG)$ and, in particular, its sub-class described in terms of the homology groups $H_2(BG;\mathbb{Z})$. Contrary to expectations we find that the defects are naturally described in terms of networks of codimension-two objects rather than isolated objects in codimension three. While in special situations linking configurations of defects are sufficient, our strategy generically predicts the existence of junctions, thus suggesting an extended applicability of the Cobordism Conjecture. We demonstrate the viability of this approach in four-dimensional supergravity theories originating from string and M-theory with a discrete Heisenberg group acting on its axionic degrees of freedom.

We investigate the finite-temperature phase diagram of polar molecules confined in a quasi-two-dimensional geometry by a harmonic potential along the polarization axis. We employ Quantum Monte Carlo simulations to explore the strongly correlated regime accessible with current experimental setups. By tuning temperature and confinement strength, we identify a rich set of phases, including normal fluid, superfluid, supersolid, cluster crystal, and bilayer crystal states. Our results reveal the emergence of crystallization upon increasing temperature, highlighting the nontrivial role of thermal fluctuations in dipolar systems. In particular, we show that a bilayer crystal with one molecule per lattice site can be stabilized by varying the confinement strength at fixed interaction. Moreover, we show evidence of layering of superfluid states with phase coherence between the two layers. These findings provide insight into the interplay between interactions, confinement, and temperature in low-dimensional dipolar systems, and suggest new directions for engineering quantum phases with ultracold polar molecules.

For a smooth projective curve of genus $g$, we study some positivity properties of (twisted) rank-$g$ Picard bundles on the $g$-fold symmetric product. As an application, we prove that the degree of irrationality of any genus $g$ Jacobian is bounded from above by $2^g$, and the degree of irrationality of any $(g-1)$-dimensional Prym variety is bounded from above by $2^{2g-3}$.

We develop a Kubo--Ando theory on order intervals of completely positive maps. Using Arveson's Radon--Nikodym theorem as a structural tool, we define relative Kubo--Ando means \(Φσ_ΩΨ\) for completely positive maps dominated by a common ambient map \(Ω\). The special choice \(Ω=Φ+Ψ\) yields an intrinsic mean of two completely positive maps. We prove that these means are independent of the chosen Stinespring representation and satisfy the expected order-theoretic properties, including monotonicity, transformer inequalities, Jensen-type inequalities, data processing, and monotonicity with respect to the ambient map. For the geometric mean, we obtain a block-positivity characterization and show that the intrinsic geometric mean vanishes exactly when the two maps have no nonzero common completely positive submap. Finally, we compare the construction with existing finite-dimensional and form-theoretic approaches: for maps between matrix algebras it agrees with the Choi-matrix mean, and in the geometric case it agrees with Okayasu's Pusz--Woronowicz mean on their common domain.

Differential dynamic microscopy (DDM) is a digital video-microscopy technique for quantitative measurements of the microscale dynamics in soft condensed matter systems. Here, multi-tau pulsed illumination DDM (MTPI-DDM) is introduced as a method for significantly enhancing the time resolution of DDM. The technique employs simple, low-cost instrumentation comprising a single monochrome digital camera and a single pulsed LED. A timing sequence, following a geometric progression of time lags, is used to generate a "multi-tau" scheme, providing high sampling density at short timescales where dynamics are fastest. In the current implementation, a time resolution of 80 $μ$s is achieved, limited by the dead time of the camera electronics. Validation of MTPI-DDM was performed by measuring the diffusion of 147 nm polystyrene nanoparticles in water. Compared to conventional continuous-wave (CW) DDM, the pulsed approach extends the range of the shortest measurable time lags by nearly two orders of magnitude and enhances DDM signal amplitudes by eliminating motion blur.

The translation from direct observables to physical properties of galaxies is a key step in reconstructing their evolutionary histories. Star-dust geometry and inhomogeneous stellar populations can induce spatial variations in the mass-to-light ratio, complicating this process. In this paper, we present tests of SE3D, a novel modelling framework built around a radiative transfer emulator, aimed at tackling this problem. We test the ability to recover known intrinsic properties of toy model and TNG50 simulated galaxies by jointly fitting mock observations of their multi-wavelength photometric and structural properties. We find an encouraging performance ($\lesssim$ 0.1 dex) for several key characteristics, including the bulk stellar mass, dust mass and SFR, as well as their respective radial extents. We point out limitations, and investigate the impact of various sources of model mismatch. Among them, mismatch in the shapes of star formation histories contributes most, with radial and azimuthal structure and stellar metallicity distributions playing a progressively more minor role. We also analyse the evolution from z=2 to z=0 of resolved stellar and dust properties of TNG galaxies, as measured intrinsically and expressed in their distribution across UVJ and IRX-$β$ diagnostic diagrams. We test different methods to assign dust to the simulation, and find a persistent lack of Mdust/Mstar evolution and a more limited dynamic range across the diagnostic diagrams compared to observations.

We revisit finite-state communicating systems with round-based communication under mailbox semantics. Mailboxes correspond to one FIFO buffer per process (instead of one buffer per pair of processes in peer-to-peer systems). Round-based communication corresponds to sequences of rounds in which processes can first send messages, then only receive (and receives must be in the same round as their sends). A system is called synchronizable if every execution can be re-scheduled into an equivalent execution that is a sequence of rounds. Previous work mostly considered the setting where rounds have fixed size. Our main contribution shows that the problem whether a mailbox communication system complies with the round-based policy, with no size limitation on rounds, is Pspace-complete. For this we use a novel automata-based approach, that also allows to determine the precise complexity (Pspace) of several questions considered in previous literature.

The availability of certain entangled resource states (catalyst states) can enhance the rate of converting several less entangled states into fewer highly entangled states in a process known as catalytic entanglement concentration (EC). Here, we extend catalytic EC from pure states to mixed states and numerically benchmark it against non-catalytic EC and distillation in the presence of state-preparation errors and operational errors. Furthermore, we analyse the re-usability of catalysts in the presence of such errors. To do this, we introduce a novel recipe for determining the positive-operator valued measurements (POVM) required for EC transformations, which allows for making tradeoffs between the number of communication rounds and the number of auxiliary qubits required. We find that in the presence of low operational errors and depolarising noise, catalytic EC can provide better rates than distillation and non-catalytic EC.

We introduce TriAlignGR, a unified multitask-multimodal framework for generative recommendation that establishes two-stage multimodal semantic propagation: (i) encoding visual semantics directly into SIDs via multimodal embeddings, and (ii) enabling the model to decode these semantics through visual description tasks. Existing Semantic ID (SID) pipelines suffer from two fundamental but underexplored problems: \textbf{SID Content Degradation (SCD)}, where cascaded encoding and residual quantization discard critical multimodal and interest-level semantics; and \textbf{SID Semantic Opacity (SSO)}, where models autoregressively generate SID sequences without truly comprehending their underlying meaning, leading to hallucination and poor generalization. Prior work addresses at most text-SID alignment, leaving visual semantics and latent user interests entirely unexploited. TriAlignGR resolves both problems through three tightly integrated components: (1)~\textbf{Cross-Modal Semantic Alignment (CMSA)} integrates visual content into SID construction through both VLM-generated textual descriptions and a multimodal embedding model that directly encodes image features alongside text, ensuring that SIDs inherently carry multimodal semantics; (2)~\textbf{Multimodal Deep Interest Mining (MDIM)} leverages LLM Chain-of-Thought reasoning to extract latent user intents (\eg ``productivity-focused lifestyle'' from noise-canceling headphones) beyond surface attributes, enriching SID semantics before discretization; and (3)~\textbf{Triangular Multitask (TMT)} jointly trains on eight complementary generation tasks under a single autoregressive loss -- including two novel visual-semantic tasks (VisDesc$\to$SID, VisDesc$\to$Title) that map VLM-generated image descriptions to SIDs and titles, completing the SID-Text-Image triangle -- without requiring task-specific towers or complex loss weighting.

We study one dimensional binary Probabilistic Cellular Automaton (PCA) that interpolate between Wolfram's classical rules 23, 77, 178 and 232. These rules are the only ones that satisfy two criteria: (i) in the case of a majority in the neighborhood states, the central site takes either the majority state or the opposite and (ii) if the neighborhood states are tied, the central site either changes its current state or keeps it. The PCA is defined by two Bernoulli random variables with parameters $p,r \in [0,1]$, and we analytically solve small size cases by using a Markov process formulation. We derive analytical expressions for the probability of asymptotically reaching each possible global configuration as a function of $p$ and $r$, for all initial states. We show that for $0 < p,r < 1$, the asymptotic probability distributions of achieving any of the states for the PCA are independent of the initial conditions. This contrasts with the behavior of the deterministic Wolfram's rules 23 ($p=0,r=0$), 77 ($p=1,r=0$), 178 ($p=0,r=1$) and 232 ($p=1,r=1$), for which additional asymptotic states can occur, in particular periodic configurations Finally, we discuss applying this kind of PCA to describe opinion dynamics involving hesitant agents.

We study the structure of the fibre operators corresponding to periodic magnetic pseudo-differential operators having periodic magnetic potentials. We obtain explicit formulas for their distribution kernel, both when these fibres are seen as operators on the $d$-dimensional torus, and also when they are seen as infinite matrices acting on a discrete $\ell^2$ space via a discrete Fourier transform. Moreover, using these distribution kernels we prove that the fibre operators are toroidal pseudo-differential operators.

Millimeter wave (mmWave) 5th generation (5G) networks offer high data rates but face coverage challenges due to severe path loss and blockage. These problems motivate the use of Integrated Access and Backhaul (IAB) as a flexible wireless backhaul solution that extends connectivity to cell boundaries and unfibered areas, including maritime environments. This paper overviews the latest 3GPP specifications for IAB networks in Releases 16 through 18. Then, it presents an ns-3 module for IAB, featuring a complete end-to-end protocol stack, including the backhaul adaptation protocol (BAP) layer, flexible slot and control configurations, and multiplexing schemes based on both time and frequency division. We test the IAB module via extensive system-level simulations in a custom maritime scenario where vessels, equipped with IAB-nodes, can simultaneously act as access points and relays, forming dynamic multi-hop networks that maintain connectivity via wireless backhaul to shore-based stations. We evaluate different topologies and channel conditions, providing insights into the design and deployment of mmWave IAB networks in offshore environments.

We reveal the effect of the spacetime parameters on the accretion morphology formed through the BHL mechanism around a slowly rotating disformal Kerr black hole. Thus, we investigate the measurable signatures of these parameters on the hydrodynamical morphology and the timing behavior of the accreting flow. It is shown that even weak disformal deviations from the Kerr solution modify the shock-cone structure, enhance the density in the post-shock region, and produce coherent oscillations in the accretion rate. The Kerr model produces coherent peaks at 42.99 Hz and 68.13 Hz, and these frequencies are consistent with the high-frequency QPOs observed from the source GRS 1915+105. In the models where the deviations from the Kerr solution are weak, low-frequency QPOs are produced and found to be coherent. These frequencies also fall within the frequency range observed in Galactic black-hole binaries. On the other hand, the models with large deviations from Kerr can be used to explain observational results that are more irregular, broad-band, and contain multiple peaks. In addition, by using inverse-mass scaling in this work, the numerically calculated frequencies are also compared with observations of intermediate-mass and supermassive black holes. In particular, the disformal black-hole models are found to be consistent with the observational results obtained from the sources M82 X-1, NGC 5408 X-1, and RE J1034+396. This comparison also allows the possible black-hole mass range of observed sources to be inferred from the relation between simulated and observed frequencies. This makes BHL accretion in disformal Kerr geometry a powerful framework for connecting modified-gravity black-hole spacetimes with observable QPO phenomenology.

Crystallization during droplet evaporation gives rise to complex, self-organized structures, yet the mechanisms underlying the emergence of ordered functional phases remain poorly understood. In this study, we present a comprehensive, multi-scale investigation into the crystallization dynamics of NaCl during droplet evaporation on a germanium (001) substrate, relevant for its IR applications. Through systematic microscopic characterization, we identify the formation of diverse microstructures, including 1D photonic crystal nanostructures formed within hybrid crystal-glass photonic system. To enable quantitative comparison across experimental conditions, we introduce the NaCl equivalent height as a unified metric to describe and classify the evolution of crystalline morphology. Our results reveal that diffusion anisotropy, rather than growth kinetics, primarily governs the maximal attainable structure size. Quantitative thin film interference analysis demonstrates the presence of discrete thickness layers in the film. Controlled evaporation experiments yield homogeneous crystallization patterns across the entire droplet area, facilitating the emergence of ordered photonic structures. Time-series dynamics analysis of height profiles uncovered the spatiotemporal evolution of the crystallization front, providing insights into the details of underlying physical mechanisms. Together, these results establish a robust experimental framework for understanding and predicting crystallization behavior in evaporating droplets, with potential applications in materials synthesis, photonics, and microscale pattern formation.

We consider a recently proposed \emph{supervised distributed computing} paradigm \cite{augustine2025supervised} that extends and refines the standard master-worker paradigm for parallel computations. In this paradigm, there is a supervisor, a source, a target, and a collection of workers. The distributed computation is given as an acyclic task graph that is known to the supervisor. The source initially stores the input and the target is supposed to store the output of the computation. The individual tasks of the computation are supposed to be executed by the workers under the guidance of the supervisor. The source, target and supervisor are assumed to be reliable, while a $β$-fraction of the workers might be adversarial, for some $β\in [0,1)$. This covers, for example, the case where a supervisor has to work with untrusted volunteers. In the standard master-worker approach, the master checks whether the workers correctly execute the assigned tasks, creating a severe bottleneck, whereas in the supervised approach, the supervisor outsources this checking to the workers. Prior to this work, only supervised solutions were known for the case that $β$ is a sufficiently small constant. We show that robust and efficient supervised solutions are possible for \emph{any} constant $β<1$ while the expected work for the honest workers is close to a \emph{single} execution per task, given that there is a lightweight verification mechanism that allows honest workers to check the correctness of task outputs, which is significantly better than all robust master-worker as well as peer-to-peer approaches known so far.

We develop an adaptive-metric framework for norm-minimization-based outer approximation algorithms in bounded convex vector optimization. The key idea is to let the scalarization metric vary across iterations while measuring approximation error in a fixed Euclidean norm. This enables the algorithm to exploit problem geometry dynamically. Our approach rests on two theoretical foundations. First, we prove that the improved Euclidean convergence rate $O(k^{2/(1-q)})$ -- previously known only for the standard $\ell_2$-norm -- extends to all fixed inner-product norms. Second, we establish a dispersion theorem showing that the cut-normals generated by the algorithm naturally spread across all directions when the upper image has a strictly convex boundary with bounded curvature. This geometric condition guarantees that the adaptive metric remains well-conditioned throughout execution. Building on these results, we derive explicit convergence bounds that quantify how metric conditioning influences the Hausdorff error estimates. Numerical experiments on three test problems validate the theoretical convergence rate; on the problems whose Pareto fronts have sufficient curvature, the adaptive metric additionally reduces the iteration count relative to the fixed Euclidean norm. Our results provide a rigorous foundation for adaptive metric selection in convex vector optimization.